Estimation and Inference with Weak, Semi-Strong, and Strong Identification

224 Pages Posted: 26 Jul 2011 Last revised: 2 Aug 2011

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Xu Cheng

University of Pennsylvania - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: July 26, 2011

Abstract

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification. This covers a class of models estimated using maximum likelihood (ML), least squares (LS), quantile, generalized method of moments (GMM), generalized empirical likelihood (GEL), minimum distance (MD), and semi-parametric estimators.

The consistency/lack-of-consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic sizes (in a uniform sense) of standard and identification-robust tests and CS's are established. The results are applied to the ARMA(1, 1) time series model estimated by ML and to the nonlinear regression model estimated by LS. In companion papers the results are applied to a number of other models.

Keywords: Asymptotic size, Confidence set, Estimator, Identification, Nonlinear models, Strong identification, Test, Weak identification

JEL Classification: C12, C15

Suggested Citation

Andrews, Donald W. K. and Cheng, Xu, Estimation and Inference with Weak, Semi-Strong, and Strong Identification (July 26, 2011). Cowles Foundation Discussion Paper No. 1773R, Available at SSRN: https://ssrn.com/abstract=1895471

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Xu Cheng

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

HOME PAGE: http://www.sas.upenn.edu/~xucheng/

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